Two taps together fill a tank in 12 hours. Working alone, the slower tap needs 10 hours more than the faster one. The faster tap alone fills the tank in:

Question

Accepted Answer

20 hours. If the faster tap takes x hours then 1/x + 1/(x + 10) = 1/12, so 12(x + 10) + 12x = x(x + 10), i.e. x² − 14x − 120 = 0. Factoring, (x − 20)(x + 6) = 0, so x = 20 (the negative root is rejected). Check: 1/20 + 1/30 = 5/60 = 1/12.

Two taps together fill a tank in 12 hours. Working alone, the slower tap needs 10 hours more than the faster one. The faster tap alone fills the tank in:

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